Analysis of Lauffenburger-Kennedy bacterial infection model for tissue inflammation dynamics.

In this paper, we analyze a mathematical model for an inflammatory response to bacterial infection of homogeneous tissues. Specifically, we provide a detailed analysis of the Lauffenburger-Kennedy bacterial infection model and show that the model exhibits three possible equilibria corresponding to a bacteria-free and two endemic compromised steady states. Asymptotic results of the steady states along with the existences of saddle-node connection Hopf bifurcations are shown under certain conditions of the parameters. Within the biological ranges of the parameter values, we observe that the system can exhibit both forward and backward bifurcation. In addition, in both cases, the larger compromise bacterial infection steady state can either approach an equilibrium or can oscillate around it via Hopf bifurcation depending on the value of the ratio of leukocyte mortality to phagocytosis rates. Numerical results are used to provide illustrative examples of these different dynamical patterns observed in the model.